Question: Solve for $x$ and $y$ using elimination. ${x-5y = -42}$ ${-4x-3y = -39}$
Answer: We can eliminate $x$ by adding the equations together when the $x$ coefficients have opposite signs. Multiply the top equation by $4$ ${4x-20y = -168}$ $-4x-3y = -39$ Add the top and bottom equations together. $-23y = -207$ $\dfrac{-23y}{{-23}} = \dfrac{-207}{{-23}}$ ${y = 9}$ Now that you know ${y = 9}$ , plug it back into $\thinspace {x-5y = -42}\thinspace$ to find $x$ ${x - 5}{(9)}{= -42}$ $x-45 = -42$ $x-45{+45} = -42{+45}$ ${x = 3}$ You can also plug ${y = 9}$ into $\thinspace {-4x-3y = -39}\thinspace$ and get the same answer for $x$ : ${-4x - 3}{(9)}{= -39}$ ${x = 3}$